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Comlan Edmond Koudjinan


Chierchia L., Koudjinan C.
V. I. Arnold's “Pointwise” KAM Theorem
2019, vol. 24, no. 6, pp.  583-606
We review V.I. Arnold's 1963 celebrated paper [1] Proof of A.N. Kolmogorov's Theorem on the Conservation of Conditionally Periodic Motions with a Small Variation in the Hamiltonian, and prove that, optimising Arnold's scheme, one can get ''sharp'' asymptotic quantitative conditions (as $\varepsilon \to 0$, $\varepsilon$ being the strength of the perturbation). All constants involved are explicitly computed.
Keywords: Nearly-integrable Hamiltonian systems, KAM theory, Arnold's Theorem, small divisors, perturbation theory, symplectic transformations
Citation: Chierchia L., Koudjinan C.,  V. I. Arnold's “Pointwise” KAM Theorem, Regular and Chaotic Dynamics, 2019, vol. 24, no. 6, pp. 583-606

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